Cold-cavity vectorial eigenmodes of VCSELs

An analytical approximate solution of Maxwell´s equations for the cold-cavity eigenmodes of cylindrical etched air-post vertical-cavity surface-emitting lasers (VCSELs) is presented. In radial and azimuthal directions, the modes correspond to the hybrid modes of cylindrical optical waveguides. A vectorial transform matrix approach is derived which takes into account coupling of bound eigenmodes in VCSEL structures. The method is illustrated for the case of noncoupled modes and the corresponding simplified transform matrix approach is used to calculate the field profiles in longitudinal direction and predict the resonance wavelengths for the VCSEL eigenmodes. Although approximate, the resulting eigenmodes may be viewed as a useful alternative to full numerical solutions, especially with regard to future more comprehensive modeling of VCSELs